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We study the abelian period sets of Sturmian words, which are codings of irrational rotations on a one-dimensional torus. The main result states that the minimum abelian period of a factor of a Sturmian word of angle α with continued fraction expansion [0; a_1, a_2, ...] is either tq_k with 1 ≤ t ≤ a_k+1 (a multiple of a denominator q_k of a convergent of α) or q_k,ℓ (a denominator q_k,ℓ of a semiconvergent of α). This result generalizes a result of Fici et. al stating that the abelian periodarXiv:1905.06138v3 fatcat:gzursxyhxzfepbjiwtgignoc7y